This paper addresses, as in Koul and Schick (1997) and Ling and McAleer (2003), adaptive and efficient estimation problems for the STAR(1) model with GARCH(1,1) errors. We use the conditions given in Koul and Schick (1997) and Ling and McAleer (2003) to derive the results. The paper is organised as follows. Section 2.1 discusses the locally asymptotically normality (LAN) of the above STAR.(1)-GARCH(1,1) errors semiparametric model. Section 2.2 addresses the question of efficient and adaptive estimation of θ, where the necessary condition for adaptive estimation, given in Koul and Schick (1997) or Ling and McAleer (2003) will be used to prove that, the STAR,(1) with GARCH(1,1) errors model is adaptive. In Section 2.3, we present simulation results to compare the conditional least squares estimate with the adaptive and efficient estimates for the STAR(1) with GARCH(1.1) errors model. Finally, the conclusion is given in Section 3. This paper uses much of the notations, definitions and results given in Koul and Schick (1997), Nur et al (2008) and Ling and McAleer (2003).

Relation

Joint Meeting of 4th World Conference of the IASC and 6th Conference of the Asian Regional Section of the IASC on Computational Statistics & Data Analysis (IASC 2008). Proceedings: IASC 2008: Joint Meeting of 4th World Conference of the IASC and 6th Conference of the Asian Regional Section of the IASC on Computational Statistics & Data Analysis (Yokohama, Japan 5-8 December, 2008) p. 1284-1290